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Block #327,136

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/24/2013, 8:14:03 AM Β· Difficulty 10.1783 Β· 6,482,319 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3f5484d55dbe9a25c9a948ad3295d2c38e89b6bc1dcb874033a3898f82dbf8aa
View on Chainz β†—

Height

#327,136

Difficulty

10.178339

Transactions

1

Size

206 B

Version

2

Bits

0a2da7a2

Nonce

29

Timestamp

12/24/2013, 8:14:03 AM

Confirmations

6,482,319

Mined by

⛏️ P2SHAbwWkWZtvvKWFxiUbZcGD749fwkawDhufa

Merkle Root

98ca4333584560afea1340b472d7c4a3bc598e6b8e3d1468c0787ed39e8e520e
Transactions (1)
Coinbase98ca4333584560…787ed39e8e520e
1 in β†’ 1 out9.6400 XPM116 B
AbwWkWZt…kawDhufa
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.

1.434 Γ— 10⁹⁡(96-digit number)
14342855285364945701…81092432096888468479
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
1.434 Γ— 10⁹⁡(96-digit number)
14342855285364945701…81092432096888468479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.434 Γ— 10⁹⁡(96-digit number)
14342855285364945701…81092432096888468481
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
2.868 Γ— 10⁹⁡(96-digit number)
28685710570729891403…62184864193776936959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.868 Γ— 10⁹⁡(96-digit number)
28685710570729891403…62184864193776936961
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
5.737 Γ— 10⁹⁡(96-digit number)
57371421141459782807…24369728387553873919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.737 Γ— 10⁹⁡(96-digit number)
57371421141459782807…24369728387553873921
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
1.147 Γ— 10⁹⁢(97-digit number)
11474284228291956561…48739456775107747839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.147 Γ— 10⁹⁢(97-digit number)
11474284228291956561…48739456775107747841
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
2.294 Γ— 10⁹⁢(97-digit number)
22948568456583913123…97478913550215495679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.294 Γ— 10⁹⁢(97-digit number)
22948568456583913123…97478913550215495681
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:57,719,711 XPMΒ·at block #6,809,454 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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