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Block #234,667

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/30/2013, 11:25:31 AM Β· Difficulty 9.9444 Β· 6,573,272 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
98aac951d4d32641230547064601ebb31442a6a507998170e0328f9fa71ecd1c
View on Chainz β†—

Height

#234,667

Difficulty

9.944363

Transactions

1

Size

200 B

Version

2

Bits

09f1c1c1

Nonce

156,234

Timestamp

10/30/2013, 11:25:31 AM

Confirmations

6,573,272

Mined by

⛏️ P2SHALVthvdBexuyeFHgma8YkVBnTzrNo2Y76q

Merkle Root

d6cb0696e011910a7e6691d5cd1f92d89e254d0ab910cef37d7f0d3f48d0ca20
Transactions (1)
Coinbased6cb0696e01191…7f0d3f48d0ca20
1 in β†’ 1 out10.1000 XPM109 B
ALVthvdB…rNo2Y76q
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.

1.463 Γ— 10⁹⁢(97-digit number)
14636926936276059528…01669362260723611199
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
1.463 Γ— 10⁹⁢(97-digit number)
14636926936276059528…01669362260723611199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.463 Γ— 10⁹⁢(97-digit number)
14636926936276059528…01669362260723611201
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
2.927 Γ— 10⁹⁢(97-digit number)
29273853872552119056…03338724521447222399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.927 Γ— 10⁹⁢(97-digit number)
29273853872552119056…03338724521447222401
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
5.854 Γ— 10⁹⁢(97-digit number)
58547707745104238113…06677449042894444799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.854 Γ— 10⁹⁢(97-digit number)
58547707745104238113…06677449042894444801
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
1.170 Γ— 10⁹⁷(98-digit number)
11709541549020847622…13354898085788889599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.170 Γ— 10⁹⁷(98-digit number)
11709541549020847622…13354898085788889601
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
2.341 Γ— 10⁹⁷(98-digit number)
23419083098041695245…26709796171577779199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.341 Γ— 10⁹⁷(98-digit number)
23419083098041695245…26709796171577779201
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:57,707,551 XPMΒ·at block #6,807,938 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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