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Block #134,588

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/26/2013, 3:14:20 AM Β· Difficulty 9.8056 Β· 6,702,342 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa7751f0633c16a0ce98e8737062896ef8ef29c808fadb54a09e958c2d36f58d
View on Chainz β†—

Height

#134,588

Difficulty

9.805570

Transactions

1

Size

207 B

Version

2

Bits

09ce39da

Nonce

533,891

Timestamp

8/26/2013, 3:14:20 AM

Confirmations

6,702,342

Mined by

⛏️ P2SHAT5A2KL6kAm5Pa3anhC8W4LVscCT16n6i2

Merkle Root

ec9c08b92d070290684fa6b776963a6c031c5cb61eca187445ab34a55f56af85
Transactions (1)
Coinbaseec9c08b92d0702…ab34a55f56af85
1 in β†’ 1 out10.3900 XPM112 B
AT5A2KL6…CT16n6i2
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.

7.634 Γ— 10¹⁰⁢(107-digit number)
76347644130201013977…34122709652531562529
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
7.634 Γ— 10¹⁰⁢(107-digit number)
76347644130201013977…34122709652531562529
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.634 Γ— 10¹⁰⁢(107-digit number)
76347644130201013977…34122709652531562531
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
1.526 Γ— 10¹⁰⁷(108-digit number)
15269528826040202795…68245419305063125059
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.526 Γ— 10¹⁰⁷(108-digit number)
15269528826040202795…68245419305063125061
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
3.053 Γ— 10¹⁰⁷(108-digit number)
30539057652080405591…36490838610126250119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.053 Γ— 10¹⁰⁷(108-digit number)
30539057652080405591…36490838610126250121
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
6.107 Γ— 10¹⁰⁷(108-digit number)
61078115304160811182…72981677220252500239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.107 Γ— 10¹⁰⁷(108-digit number)
61078115304160811182…72981677220252500241
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
1.221 Γ— 10¹⁰⁸(109-digit number)
12215623060832162236…45963354440505000479
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:57,939,736 XPMΒ·at block #6,836,929 Β· updates every 60s
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