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Block #357,420

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/13/2014, 9:59:33 AM Β· Difficulty 10.3830 Β· 6,453,683 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b467f71641b0fe088f069d41059c9b3da692d1b326744e8dc9cecab4d996cc4d
View on Chainz β†—

Height

#357,420

Difficulty

10.382957

Transactions

1

Size

200 B

Version

2

Bits

0a62097c

Nonce

117,040

Timestamp

1/13/2014, 9:59:33 AM

Confirmations

6,453,683

Mined by

⛏️ P2SHAbWzNQQfdk7tsLEZbLbmi1xqR4bAY9RJig

Merkle Root

bd44b54d89607fec51e6917d0a3793d7ae7da10041d6acea2d73e9da1ac0d505
Transactions (1)
Coinbasebd44b54d89607f…73e9da1ac0d505
1 in β†’ 1 out9.2600 XPM109 B
AbWzNQQf…bAY9RJig
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.

3.244 Γ— 10⁹⁷(98-digit number)
32440386482175396809…11059520012078750399
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
3.244 Γ— 10⁹⁷(98-digit number)
32440386482175396809…11059520012078750399
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.244 Γ— 10⁹⁷(98-digit number)
32440386482175396809…11059520012078750401
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
6.488 Γ— 10⁹⁷(98-digit number)
64880772964350793619…22119040024157500799
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.488 Γ— 10⁹⁷(98-digit number)
64880772964350793619…22119040024157500801
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
1.297 Γ— 10⁹⁸(99-digit number)
12976154592870158723…44238080048315001599
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.297 Γ— 10⁹⁸(99-digit number)
12976154592870158723…44238080048315001601
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
2.595 Γ— 10⁹⁸(99-digit number)
25952309185740317447…88476160096630003199
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.595 Γ— 10⁹⁸(99-digit number)
25952309185740317447…88476160096630003201
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
5.190 Γ— 10⁹⁸(99-digit number)
51904618371480634895…76952320193260006399
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.190 Γ— 10⁹⁸(99-digit number)
51904618371480634895…76952320193260006401
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:57,732,931 XPMΒ·at block #6,811,102 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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