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Block #469,216

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 4/1/2014, 1:50:06 AM Β· Difficulty 10.4289 Β· 6,345,835 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
05303e12b747af3434d223beb96ba6bc0e58254ca1cd52749aea7599d44839d8
View on Chainz β†—

Height

#469,216

Difficulty

10.428946

Transactions

1

Size

203 B

Version

2

Bits

0a6dcf64

Nonce

418,678

Timestamp

4/1/2014, 1:50:06 AM

Confirmations

6,345,835

Mined by

⛏️ P2SHAPJB1YGAgReatMzCRPMXLzfRBYQWLCeuQW

Merkle Root

b7ae5170dbeec26d4fe5277cece8cf983b90d5fe641f9037d1bd648c83567629
Transactions (1)
Coinbaseb7ae5170dbeec2…bd648c83567629
1 in β†’ 1 out9.1800 XPM111 B
APJB1YGA…QWLCeuQW
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.

9.907 Γ— 10⁹⁸(99-digit number)
99073445088314810078…04213392403325624319
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
9.907 Γ— 10⁹⁸(99-digit number)
99073445088314810078…04213392403325624319
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.907 Γ— 10⁹⁸(99-digit number)
99073445088314810078…04213392403325624321
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
1.981 Γ— 10⁹⁹(100-digit number)
19814689017662962015…08426784806651248639
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.981 Γ— 10⁹⁹(100-digit number)
19814689017662962015…08426784806651248641
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
3.962 Γ— 10⁹⁹(100-digit number)
39629378035325924031…16853569613302497279
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.962 Γ— 10⁹⁹(100-digit number)
39629378035325924031…16853569613302497281
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
7.925 Γ— 10⁹⁹(100-digit number)
79258756070651848062…33707139226604994559
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.925 Γ— 10⁹⁹(100-digit number)
79258756070651848062…33707139226604994561
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
1.585 Γ— 10¹⁰⁰(101-digit number)
15851751214130369612…67414278453209989119
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.585 Γ— 10¹⁰⁰(101-digit number)
15851751214130369612…67414278453209989121
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:57,764,499 XPMΒ·at block #6,815,050 Β· updates every 60s
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