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Block #99,944

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/5/2013, 10:30:09 PM Β· Difficulty 9.4077 Β· 6,716,689 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
678671655f967528f8f0b6db7ccfee93785f93ad05792b2521cc7df0f8843f90
View on Chainz β†—

Height

#99,944

Difficulty

9.407655

Transactions

1

Size

200 B

Version

2

Bits

09685c12

Nonce

42,847

Timestamp

8/5/2013, 10:30:09 PM

Confirmations

6,716,689

Mined by

⛏️ P2SHAXvMMum1Pa5kWMWJFC5uKC4CTEy1ajpFRb

Merkle Root

6712b90a4aa37191950f8c334ea349cd5aa67dece3ac0bc2f2c670e6d2a482ef
Transactions (1)
Coinbase6712b90a4aa371…c670e6d2a482ef
1 in β†’ 1 out11.2800 XPM109 B
AXvMMum1…y1ajpFRb
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.

9.320 Γ— 10⁹⁷(98-digit number)
93203185040127611808…28471847523469790079
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
9.320 Γ— 10⁹⁷(98-digit number)
93203185040127611808…28471847523469790079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.320 Γ— 10⁹⁷(98-digit number)
93203185040127611808…28471847523469790081
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
1.864 Γ— 10⁹⁸(99-digit number)
18640637008025522361…56943695046939580159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.864 Γ— 10⁹⁸(99-digit number)
18640637008025522361…56943695046939580161
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
3.728 Γ— 10⁹⁸(99-digit number)
37281274016051044723…13887390093879160319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.728 Γ— 10⁹⁸(99-digit number)
37281274016051044723…13887390093879160321
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
7.456 Γ— 10⁹⁸(99-digit number)
74562548032102089446…27774780187758320639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.456 Γ— 10⁹⁸(99-digit number)
74562548032102089446…27774780187758320641
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
1.491 Γ— 10⁹⁹(100-digit number)
14912509606420417889…55549560375516641279
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:57,777,179 XPMΒ·at block #6,816,632 Β· updates every 60s
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