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Block #303,840

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/10/2013, 2:33:18 PM Β· Difficulty 9.9931 Β· 6,492,974 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
42cfbab74477cd62030ae9548818c841f304f0a292927416fe6fcc6885c46c27
View on Chainz β†—

Height

#303,840

Difficulty

9.993142

Transactions

1

Size

1004 B

Version

2

Bits

09fe3e96

Nonce

15,788

Timestamp

12/10/2013, 2:33:18 PM

Confirmations

6,492,974

Mined by

⛏️ aR&.{AdHLg17tC6HEqeFWE8BbtTqonV3tfs38KT

Merkle Root

75309639588942600f1517e86af0e67bcb70f7d121b352b8f9c58ae9ddde20f6
Transactions (1)
Coinbase75309639588942…c58ae9ddde20f6
1 in β†’ 25 out10.0000 XPM913 B
AdHLg17t…3tfs38KTAJzWx2VD…j4ZSMit5AdVgkWdJ…YY3Q4dueAWZd1qVJ…9pj9yfPaAcM3ext6…Hwtj9Qp3
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.

2.145 Γ— 10⁹⁢(97-digit number)
21457801670213429627…45431152326086021119
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
2.145 Γ— 10⁹⁢(97-digit number)
21457801670213429627…45431152326086021119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.145 Γ— 10⁹⁢(97-digit number)
21457801670213429627…45431152326086021121
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
4.291 Γ— 10⁹⁢(97-digit number)
42915603340426859255…90862304652172042239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.291 Γ— 10⁹⁢(97-digit number)
42915603340426859255…90862304652172042241
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
8.583 Γ— 10⁹⁢(97-digit number)
85831206680853718511…81724609304344084479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.583 Γ— 10⁹⁢(97-digit number)
85831206680853718511…81724609304344084481
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
1.716 Γ— 10⁹⁷(98-digit number)
17166241336170743702…63449218608688168959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.716 Γ— 10⁹⁷(98-digit number)
17166241336170743702…63449218608688168961
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
3.433 Γ— 10⁹⁷(98-digit number)
34332482672341487404…26898437217376337919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.433 Γ— 10⁹⁷(98-digit number)
34332482672341487404…26898437217376337921
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:57,618,520 XPMΒ·at block #6,796,813 Β· updates every 60s
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