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Block #83,654

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/26/2013, 7:30:53 AM Β· Difficulty 9.2679 Β· 6,710,834 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
fa72dbb990beec0aa386a7f57ee43e6b611dab4237fb52e8a4c230a329768023
View on Chainz β†—

Height

#83,654

Difficulty

9.267886

Transactions

1

Size

204 B

Version

2

Bits

0944942d

Nonce

277,817

Timestamp

7/26/2013, 7:30:53 AM

Confirmations

6,710,834

Mined by

⛏️ P2SHAcuJraLTi7SA51dYsYdywtXJwqY66BS47Q

Merkle Root

bdbd814baf10b630ab2eac16f3565d2e6ef84eb79e7c04c3639020d4fcd33aca
Transactions (1)
Coinbasebdbd814baf10b6…9020d4fcd33aca
1 in β†’ 1 out11.6300 XPM109 B
AcuJraLT…Y66BS47Q
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.

8.815 Γ— 10¹⁰⁢(107-digit number)
88154650763836232089…04262068418648176529
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
8.815 Γ— 10¹⁰⁢(107-digit number)
88154650763836232089…04262068418648176529
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.815 Γ— 10¹⁰⁢(107-digit number)
88154650763836232089…04262068418648176531
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
1.763 Γ— 10¹⁰⁷(108-digit number)
17630930152767246417…08524136837296353059
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.763 Γ— 10¹⁰⁷(108-digit number)
17630930152767246417…08524136837296353061
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
3.526 Γ— 10¹⁰⁷(108-digit number)
35261860305534492835…17048273674592706119
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.526 Γ— 10¹⁰⁷(108-digit number)
35261860305534492835…17048273674592706121
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
7.052 Γ— 10¹⁰⁷(108-digit number)
70523720611068985671…34096547349185412239
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.052 Γ— 10¹⁰⁷(108-digit number)
70523720611068985671…34096547349185412241
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
1.410 Γ— 10¹⁰⁸(109-digit number)
14104744122213797134…68193094698370824479
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:57,599,939 XPMΒ·at block #6,794,487 Β· updates every 60s
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