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Block #248,700

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/7/2013, 1:02:00 PM Β· Difficulty 9.9660 Β· 6,590,546 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
46ef652aa5ac65c89d9be84e2e87835710213bf07c56ebf439d4747c1444e64b
View on Chainz β†—

Height

#248,700

Difficulty

9.966031

Transactions

1

Size

205 B

Version

2

Bits

09f74dd5

Nonce

70,733

Timestamp

11/7/2013, 1:02:00 PM

Confirmations

6,590,546

Mined by

⛏️ P2SHAcLBm5Z9BD7o7btAchFh9KZEkSS683d7c3

Merkle Root

986485d60e02a2e602d2d82d4dea14cc67f191bab48305bb623cfdf91257062e
Transactions (1)
Coinbase986485d60e02a2…3cfdf91257062e
1 in β†’ 1 out10.0500 XPM116 B
AcLBm5Z9…S683d7c3
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.

2.267 Γ— 10⁹³(94-digit number)
22676628964518959363…36724234899189166079
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
2.267 Γ— 10⁹³(94-digit number)
22676628964518959363…36724234899189166079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.267 Γ— 10⁹³(94-digit number)
22676628964518959363…36724234899189166081
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
4.535 Γ— 10⁹³(94-digit number)
45353257929037918726…73448469798378332159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.535 Γ— 10⁹³(94-digit number)
45353257929037918726…73448469798378332161
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
9.070 Γ— 10⁹³(94-digit number)
90706515858075837453…46896939596756664319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.070 Γ— 10⁹³(94-digit number)
90706515858075837453…46896939596756664321
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
1.814 Γ— 10⁹⁴(95-digit number)
18141303171615167490…93793879193513328639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.814 Γ— 10⁹⁴(95-digit number)
18141303171615167490…93793879193513328641
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
3.628 Γ— 10⁹⁴(95-digit number)
36282606343230334981…87587758387026657279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.628 Γ— 10⁹⁴(95-digit number)
36282606343230334981…87587758387026657281
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,958,251 XPMΒ·at block #6,839,245 Β· updates every 60s
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