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Block #399,384

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/11/2014, 9:36:16 AM Β· Difficulty 10.4238 Β· 6,410,576 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
56bf0b0cc74fe7f816cdaa3e8cf5e233d217da595d4d2993a9871f111bd1a9fe
View on Chainz β†—

Height

#399,384

Difficulty

10.423829

Transactions

1

Size

203 B

Version

2

Bits

0a6c8008

Nonce

49,457

Timestamp

2/11/2014, 9:36:16 AM

Confirmations

6,410,576

Mined by

⛏️ P2SHARBRYiL8QjnU5zrwTmS3JgwVXJoj38gY3N

Merkle Root

8d3b62f24fd0a1f32d73845923af2a0231382cdacd8953c75ee4d6025e9f857c
Transactions (1)
Coinbase8d3b62f24fd0a1…e4d6025e9f857c
1 in β†’ 1 out9.1900 XPM111 B
ARBRYiL8…oj38gY3N
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.

2.944 Γ— 10¹⁰⁰(101-digit number)
29445589640309219792…20690823391756031999
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
2.944 Γ— 10¹⁰⁰(101-digit number)
29445589640309219792…20690823391756031999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.944 Γ— 10¹⁰⁰(101-digit number)
29445589640309219792…20690823391756032001
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
5.889 Γ— 10¹⁰⁰(101-digit number)
58891179280618439584…41381646783512063999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.889 Γ— 10¹⁰⁰(101-digit number)
58891179280618439584…41381646783512064001
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
1.177 Γ— 10¹⁰¹(102-digit number)
11778235856123687916…82763293567024127999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.177 Γ— 10¹⁰¹(102-digit number)
11778235856123687916…82763293567024128001
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
2.355 Γ— 10¹⁰¹(102-digit number)
23556471712247375833…65526587134048255999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.355 Γ— 10¹⁰¹(102-digit number)
23556471712247375833…65526587134048256001
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
4.711 Γ— 10¹⁰¹(102-digit number)
47112943424494751667…31053174268096511999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.711 Γ— 10¹⁰¹(102-digit number)
47112943424494751667…31053174268096512001
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:57,723,752 XPMΒ·at block #6,809,959 Β· updates every 60s
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