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Block #126,531

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/20/2013, 10:33:32 PM Β· Difficulty 9.7817 Β· 6,669,613 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dc3898e666dc742f3e742118ba6dcde07a5f7902b3a83c4acd0ccb70b1acb2e4
View on Chainz β†—

Height

#126,531

Difficulty

9.781732

Transactions

1

Size

200 B

Version

2

Bits

09c81f98

Nonce

187,109

Timestamp

8/20/2013, 10:33:32 PM

Confirmations

6,669,613

Mined by

⛏️ P2SHAZWM4ekziWKzqfvkDKCd9qFuagMir2NEyg

Merkle Root

3133701540206344035ee164d016756cacd42320967e2a9ab483fbf17a208939
Transactions (1)
Coinbase31337015402063…83fbf17a208939
1 in β†’ 1 out10.4400 XPM109 B
AZWM4ekz…Mir2NEyg
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.

5.623 Γ— 10⁹⁢(97-digit number)
56237271466531532973…98332732505051555199
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
5.623 Γ— 10⁹⁢(97-digit number)
56237271466531532973…98332732505051555199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.623 Γ— 10⁹⁢(97-digit number)
56237271466531532973…98332732505051555201
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
1.124 Γ— 10⁹⁷(98-digit number)
11247454293306306594…96665465010103110399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.124 Γ— 10⁹⁷(98-digit number)
11247454293306306594…96665465010103110401
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
2.249 Γ— 10⁹⁷(98-digit number)
22494908586612613189…93330930020206220799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.249 Γ— 10⁹⁷(98-digit number)
22494908586612613189…93330930020206220801
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
4.498 Γ— 10⁹⁷(98-digit number)
44989817173225226378…86661860040412441599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.498 Γ— 10⁹⁷(98-digit number)
44989817173225226378…86661860040412441601
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
8.997 Γ— 10⁹⁷(98-digit number)
89979634346450452757…73323720080824883199
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 9 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
CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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:57,613,149 XPMΒ·at block #6,796,143 Β· updates every 60s
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