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Block #28,509

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 7/13/2013, 12:30:17 PM Β· Difficulty 7.9821 Β· 6,767,861 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
cbc3cd1ca2dcc2090a1c18042bb84875008dd6dad4bad332186bbb5b4e731e96
View on Chainz β†—

Height

#28,509

Difficulty

7.982135

Transactions

2

Size

354 B

Version

2

Bits

07fb6d2c

Nonce

1,060

Timestamp

7/13/2013, 12:30:17 PM

Confirmations

6,767,861

Mined by

⛏️ P2SHALuCK1YgWxfq9UtJRLJGE5NeRbXqMp1DZg

Merkle Root

27667ac0d0e9c7ba636d6ca3bbfb669f6b3c6aa0188873ccd85e867e89ad72b8
Transactions (2)
Coinbase447c1a936ec6be…b01e8ca0792f89
1 in β†’ 1 out15.6800 XPM108 B
ALuCK1Yg…XqMp1DZg
21582541c678f2…1b896e252e0b88
1 in β†’ 1 out15.7600 XPM158 B
AU4AxAzL…y8DH19oQ
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.

1.677 Γ— 10⁹⁰(91-digit number)
16774330233700740210…65738479587925787999
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
1.677 Γ— 10⁹⁰(91-digit number)
16774330233700740210…65738479587925787999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.677 Γ— 10⁹⁰(91-digit number)
16774330233700740210…65738479587925788001
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
3.354 Γ— 10⁹⁰(91-digit number)
33548660467401480420…31476959175851575999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.354 Γ— 10⁹⁰(91-digit number)
33548660467401480420…31476959175851576001
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
6.709 Γ— 10⁹⁰(91-digit number)
67097320934802960841…62953918351703151999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.709 Γ— 10⁹⁰(91-digit number)
67097320934802960841…62953918351703152001
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
1.341 Γ— 10⁹¹(92-digit number)
13419464186960592168…25907836703406303999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.341 Γ— 10⁹¹(92-digit number)
13419464186960592168…25907836703406304001
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
2.683 Γ— 10⁹¹(92-digit number)
26838928373921184336…51815673406812607999
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:57,614,954 XPMΒ·at block #6,796,369 Β· updates every 60s
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