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Block #29,113

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 2:25:22 PM Β· Difficulty 7.9838 Β· 6,780,669 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4ecbde99ee5c0b1716b8b58b048af5e003bc265583ab50c768823c24a0b32ed4
View on Chainz β†—

Height

#29,113

Difficulty

7.983803

Transactions

1

Size

199 B

Version

2

Bits

07fbda80

Nonce

341

Timestamp

7/13/2013, 2:25:22 PM

Confirmations

6,780,669

Mined by

⛏️ P2SHAGemJXng9Py5jf5TzegELEhNUUw1K3MEut

Merkle Root

9187bcc93272642329b4fe780ccdf00a973b7385d17febb2e7938294d82f269e
Transactions (1)
Coinbase9187bcc9327264…938294d82f269e
1 in β†’ 1 out15.6700 XPM108 B
AGemJXng…w1K3MEut
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.

1.339 Γ— 10⁹⁸(99-digit number)
13397039026490705822…31259518849132511839
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
1.339 Γ— 10⁹⁸(99-digit number)
13397039026490705822…31259518849132511839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.339 Γ— 10⁹⁸(99-digit number)
13397039026490705822…31259518849132511841
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
2.679 Γ— 10⁹⁸(99-digit number)
26794078052981411644…62519037698265023679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.679 Γ— 10⁹⁸(99-digit number)
26794078052981411644…62519037698265023681
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
5.358 Γ— 10⁹⁸(99-digit number)
53588156105962823288…25038075396530047359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.358 Γ— 10⁹⁸(99-digit number)
53588156105962823288…25038075396530047361
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
1.071 Γ— 10⁹⁹(100-digit number)
10717631221192564657…50076150793060094719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.071 Γ— 10⁹⁹(100-digit number)
10717631221192564657…50076150793060094721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 8 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 8

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:57,722,335 XPMΒ·at block #6,809,781 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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