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Block #539,686

TWNLength 12β˜…β˜…β˜…β˜…β˜†

Bi-Twin Chain Β· Discovered 5/12/2014, 8:07:08 PM Β· Difficulty 10.9293 Β· 6,256,801 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
b1728a2b1da9f6a79a52ac7bdccaf3923657e3db17ca24591a2c250860c0f074
View on Chainz β†—

Height

#539,686

Difficulty

10.929311

Transactions

2

Size

2.99 KB

Version

2

Bits

0aede758

Nonce

152,484,441

Timestamp

5/12/2014, 8:07:08 PM

Confirmations

6,256,801

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

7f99086fdadf7c2ba2404c378da929abee2b47e7baa8d75970566082a89de6a8
Transactions (2)
Coinbaseed9ba95f14752a…2288a85cd1f668
1 in β†’ 1 out8.3900 XPM116 B
ANSXnLY2…Sd25TjkD
8d127a934734b9…a9a477b4819268
19 in β†’ 1 out57.0788 XPM2.79 KB
AYfGXBG3…s4uNnsy3
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.073 Γ— 10⁹⁷(98-digit number)
60732321415898183583…51354752286402409949
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.073 Γ— 10⁹⁷(98-digit number)
60732321415898183583…51354752286402409949
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.073 Γ— 10⁹⁷(98-digit number)
60732321415898183583…51354752286402409951
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.214 Γ— 10⁹⁸(99-digit number)
12146464283179636716…02709504572804819899
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.214 Γ— 10⁹⁸(99-digit number)
12146464283179636716…02709504572804819901
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.429 Γ— 10⁹⁸(99-digit number)
24292928566359273433…05419009145609639799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.429 Γ— 10⁹⁸(99-digit number)
24292928566359273433…05419009145609639801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
4.858 Γ— 10⁹⁸(99-digit number)
48585857132718546867…10838018291219279599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.858 Γ— 10⁹⁸(99-digit number)
48585857132718546867…10838018291219279601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
9.717 Γ— 10⁹⁸(99-digit number)
97171714265437093734…21676036582438559199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.717 Γ— 10⁹⁸(99-digit number)
97171714265437093734…21676036582438559201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.943 Γ— 10⁹⁹(100-digit number)
19434342853087418746…43352073164877118399
Verify on FactorDB β†—Wolfram Alpha β†—
2^5 Γ— origin + 1
1.943 Γ— 10⁹⁹(100-digit number)
19434342853087418746…43352073164877118401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^5 Γ— origin + 1 βˆ’ 2^5 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 12 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜…β˜…β˜†
Rarity
ExceptionalChain length 12

Around 1 in 10,000 blocks. A significant mathematical achievement.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,615,894 XPMΒ·at block #6,796,486 Β· updates every 60s
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