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Block #269,025

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/22/2013, 4:08:30 PM Β· Difficulty 9.9556 Β· 6,540,219 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e46b1f339f9b8473e2b9159b973913f04db43e56ad172dd68b5997172aa7805c
View on Chainz β†—

Height

#269,025

Difficulty

9.955648

Transactions

1

Size

198 B

Version

2

Bits

09f4a555

Nonce

42,356

Timestamp

11/22/2013, 4:08:30 PM

Confirmations

6,540,219

Mined by

⛏️ P2SHAab2HB2z57Nnnmg2yTJeqwdmWCoocYKQJE

Merkle Root

6c9cf5784e259f754601f3105d753a59a131ee71e915cb31b0c146d69502f599
Transactions (1)
Coinbase6c9cf5784e259f…c146d69502f599
1 in β†’ 1 out10.0700 XPM109 B
Aab2HB2z…oocYKQJE
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.

3.462 Γ— 10⁹³(94-digit number)
34622376249140826663…15502422363173167519
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
3.462 Γ— 10⁹³(94-digit number)
34622376249140826663…15502422363173167519
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.462 Γ— 10⁹³(94-digit number)
34622376249140826663…15502422363173167521
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
6.924 Γ— 10⁹³(94-digit number)
69244752498281653327…31004844726346335039
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.924 Γ— 10⁹³(94-digit number)
69244752498281653327…31004844726346335041
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
1.384 Γ— 10⁹⁴(95-digit number)
13848950499656330665…62009689452692670079
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.384 Γ— 10⁹⁴(95-digit number)
13848950499656330665…62009689452692670081
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
2.769 Γ— 10⁹⁴(95-digit number)
27697900999312661331…24019378905385340159
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.769 Γ— 10⁹⁴(95-digit number)
27697900999312661331…24019378905385340161
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
5.539 Γ— 10⁹⁴(95-digit number)
55395801998625322662…48038757810770680319
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:57,718,018 XPMΒ·at block #6,809,243 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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