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Block #26,987

TWNLength 8β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 7:15:29 AM Β· Difficulty 7.9772 Β· 6,784,121 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
35289b779c1d174e6cbad0f614e5dec27ff1b0caab64985fcd058bf52ff5191f
View on Chainz β†—

Height

#26,987

Difficulty

7.977248

Transactions

1

Size

197 B

Version

2

Bits

07fa2cef

Nonce

513

Timestamp

7/13/2013, 7:15:29 AM

Confirmations

6,784,121

Mined by

⛏️ P2SHAdLHjXsUty49dgVJZ3aPvJsZozoW2p61uB

Merkle Root

1a08b0af81eb8849d69de37ea92b95c40d452bd1bded21fc6a54db0f79becabf
Transactions (1)
Coinbase1a08b0af81eb88…54db0f79becabf
1 in β†’ 1 out15.6900 XPM108 B
AdLHjXsU…oW2p61uB
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.

2.397 Γ— 10⁹³(94-digit number)
23974711755049777994…44617851684399130359
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
2.397 Γ— 10⁹³(94-digit number)
23974711755049777994…44617851684399130359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.397 Γ— 10⁹³(94-digit number)
23974711755049777994…44617851684399130361
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
4.794 Γ— 10⁹³(94-digit number)
47949423510099555989…89235703368798260719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.794 Γ— 10⁹³(94-digit number)
47949423510099555989…89235703368798260721
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
9.589 Γ— 10⁹³(94-digit number)
95898847020199111978…78471406737596521439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.589 Γ— 10⁹³(94-digit number)
95898847020199111978…78471406737596521441
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
1.917 Γ— 10⁹⁴(95-digit number)
19179769404039822395…56942813475193042879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.917 Γ— 10⁹⁴(95-digit number)
19179769404039822395…56942813475193042881
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:57,732,971 XPMΒ·at block #6,811,107 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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