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Block #586,772

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/13/2014, 7:02:22 AM Β· Difficulty 10.9524 Β· 6,229,774 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9acd8aaf785cc7a352f811b9e22a80a01e4850dbcacd835b2bd9504fa0e909b8
View on Chainz β†—

Height

#586,772

Difficulty

10.952367

Transactions

1

Size

208 B

Version

2

Bits

0af3ce57

Nonce

1,843,038,292

Timestamp

6/13/2014, 7:02:22 AM

Confirmations

6,229,774

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2b669ce0717bcbb12d762928e50531718e71b1989340c84692779988657c89d4
Transactions (1)
Coinbase2b669ce0717bcb…779988657c89d4
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
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.

4.656 Γ— 10⁹⁸(99-digit number)
46569339882690228356…98564213049591546239
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
4.656 Γ— 10⁹⁸(99-digit number)
46569339882690228356…98564213049591546239
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.656 Γ— 10⁹⁸(99-digit number)
46569339882690228356…98564213049591546241
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
9.313 Γ— 10⁹⁸(99-digit number)
93138679765380456712…97128426099183092479
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.313 Γ— 10⁹⁸(99-digit number)
93138679765380456712…97128426099183092481
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
1.862 Γ— 10⁹⁹(100-digit number)
18627735953076091342…94256852198366184959
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.862 Γ— 10⁹⁹(100-digit number)
18627735953076091342…94256852198366184961
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
3.725 Γ— 10⁹⁹(100-digit number)
37255471906152182685…88513704396732369919
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.725 Γ— 10⁹⁹(100-digit number)
37255471906152182685…88513704396732369921
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
7.451 Γ— 10⁹⁹(100-digit number)
74510943812304365370…77027408793464739839
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.451 Γ— 10⁹⁹(100-digit number)
74510943812304365370…77027408793464739841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,776,497 XPMΒ·at block #6,816,545 Β· updates every 60s
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