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Block #91,131

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/31/2013, 5:13:46 PM Β· Difficulty 9.2226 Β· 6,735,626 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1dc4a8e74b80aeda2505a2fbc2dd4c2334cea64cde6d379bb774dee62f2ca1b2
View on Chainz β†—

Height

#91,131

Difficulty

9.222591

Transactions

1

Size

202 B

Version

2

Bits

0938fbb7

Nonce

858

Timestamp

7/31/2013, 5:13:46 PM

Confirmations

6,735,626

Mined by

⛏️ P2SHAPY1J1ZY3DzGhusFBRaTCuTgUHFaUv3anE

Merkle Root

bdb89889d4ba3dfeddac27f42a5d0ec213efd4b5ad3706e87c6d0300f2d8db5c
Transactions (1)
Coinbasebdb89889d4ba3d…6d0300f2d8db5c
1 in β†’ 1 out11.7400 XPM110 B
APY1J1ZY…FaUv3anE
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.

3.684 Γ— 10⁹⁹(100-digit number)
36848732178742834380…34156635947878555359
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
3.684 Γ— 10⁹⁹(100-digit number)
36848732178742834380…34156635947878555359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.684 Γ— 10⁹⁹(100-digit number)
36848732178742834380…34156635947878555361
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
7.369 Γ— 10⁹⁹(100-digit number)
73697464357485668761…68313271895757110719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.369 Γ— 10⁹⁹(100-digit number)
73697464357485668761…68313271895757110721
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
1.473 Γ— 10¹⁰⁰(101-digit number)
14739492871497133752…36626543791514221439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.473 Γ— 10¹⁰⁰(101-digit number)
14739492871497133752…36626543791514221441
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
2.947 Γ— 10¹⁰⁰(101-digit number)
29478985742994267504…73253087583028442879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.947 Γ— 10¹⁰⁰(101-digit number)
29478985742994267504…73253087583028442881
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
5.895 Γ— 10¹⁰⁰(101-digit number)
58957971485988535009…46506175166056885759
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:57,858,214 XPMΒ·at block #6,826,756 Β· updates every 60s
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