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Block #203,832

TWNLength 9β˜…β˜†β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 10/11/2013, 2:58:13 AM Β· Difficulty 9.8975 Β· 6,599,541 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
816339f24f2e853e683c7e63153f2fd3c73a2585f64f732f94ee7fd3891c5840
View on Chainz β†—

Height

#203,832

Difficulty

9.897495

Transactions

1

Size

197 B

Version

2

Bits

09e5c23d

Nonce

3,646

Timestamp

10/11/2013, 2:58:13 AM

Confirmations

6,599,541

Mined by

⛏️ P2SHAK9vVy2joHqUBrbiHFhRPZZcZJniNoc5U8

Merkle Root

b2e4e550a6dd29fde79a0453ac680792dd2089a3576589fc2aadbc1fc66bbc57
Transactions (1)
Coinbaseb2e4e550a6dd29…adbc1fc66bbc57
1 in β†’ 1 out10.1900 XPM109 B
AK9vVy2j…niNoc5U8
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.

3.816 Γ— 10⁹⁰(91-digit number)
38168146807160358556…13162876317005101599
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
3.816 Γ— 10⁹⁰(91-digit number)
38168146807160358556…13162876317005101599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.816 Γ— 10⁹⁰(91-digit number)
38168146807160358556…13162876317005101601
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
7.633 Γ— 10⁹⁰(91-digit number)
76336293614320717113…26325752634010203199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.633 Γ— 10⁹⁰(91-digit number)
76336293614320717113…26325752634010203201
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
1.526 Γ— 10⁹¹(92-digit number)
15267258722864143422…52651505268020406399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.526 Γ— 10⁹¹(92-digit number)
15267258722864143422…52651505268020406401
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
3.053 Γ— 10⁹¹(92-digit number)
30534517445728286845…05303010536040812799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.053 Γ— 10⁹¹(92-digit number)
30534517445728286845…05303010536040812801
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
6.106 Γ— 10⁹¹(92-digit number)
61069034891456573690…10606021072081625599
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:57,671,020 XPMΒ·at block #6,803,372 Β· updates every 60s
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