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Block #648,477

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2014, 8:20:50 AM Β· Difficulty 10.9515 Β· 6,176,285 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
d9c28aa9ae3eaa900e556451e52ea96ea2cff0acc116ec01be134d8db2c0ea45
View on Chainz β†—

Height

#648,477

Difficulty

10.951471

Transactions

2

Size

10.68 KB

Version

2

Bits

0af39394

Nonce

283,269,903

Timestamp

7/26/2014, 8:20:50 AM

Confirmations

6,176,285

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

b658759c54f407067a370129381bcc9e9c3284832ad2092d5a1fe920f5c24c39
Transactions (2)
Coinbase1ba318c9fcc959…1ad67e639cd49b
1 in β†’ 1 out8.4300 XPM116 B
ANSXnLY2…Sd25TjkD
929536990e1320…35f3889194bb4e
72 in β†’ 2 out40.0100 XPM10.48 KB
APP97DSB…Wfj7mmNuAaw7CsXd…VxcmraZL
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.

1.188 Γ— 10⁹⁢(97-digit number)
11880045680931835234…62817088261361425919
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
1.188 Γ— 10⁹⁢(97-digit number)
11880045680931835234…62817088261361425919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.188 Γ— 10⁹⁢(97-digit number)
11880045680931835234…62817088261361425921
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
2.376 Γ— 10⁹⁢(97-digit number)
23760091361863670468…25634176522722851839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.376 Γ— 10⁹⁢(97-digit number)
23760091361863670468…25634176522722851841
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
4.752 Γ— 10⁹⁢(97-digit number)
47520182723727340937…51268353045445703679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.752 Γ— 10⁹⁢(97-digit number)
47520182723727340937…51268353045445703681
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
9.504 Γ— 10⁹⁢(97-digit number)
95040365447454681875…02536706090891407359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.504 Γ— 10⁹⁢(97-digit number)
95040365447454681875…02536706090891407361
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
1.900 Γ— 10⁹⁷(98-digit number)
19008073089490936375…05073412181782814719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.900 Γ— 10⁹⁷(98-digit number)
19008073089490936375…05073412181782814721
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
3.801 Γ— 10⁹⁷(98-digit number)
38016146178981872750…10146824363565629439
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,842,168 XPMΒ·at block #6,824,761 Β· updates every 60s
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