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Block #2,237,072

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/4/2017, 8:02:34 PM Β· Difficulty 10.9463 Β· 4,601,031 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
acca00bff8ceabd06999b31f67b2f28375ce8a347f7d99471fea71e84591a3ad
View on Chainz β†—

Height

#2,237,072

Difficulty

10.946340

Transactions

2

Size

722 B

Version

2

Bits

0af2435c

Nonce

170,323,797

Timestamp

8/4/2017, 8:02:34 PM

Confirmations

4,601,031

Mined by

⛏️ P2SHAHby2ScmbNd6v3HQNQ34FwR7AB5wEosUcq

Merkle Root

cf2a9a007f635f6defad7f5b8eaea24a5bdb96cce6621c2b8605b875ea5e6df9
Transactions (2)
Coinbase0651b2393857b6…251fcd3e0cafbc
1 in β†’ 1 out8.3400 XPM110 B
AHby2Scm…5wEosUcq
3db88280d978b3…7be01c783df9fe
3 in β†’ 2 out2.0361 XPM523 B
AWKPytVA…eQ7q2RydATcQ9fcb…m2R4Z2pZ
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.

2.237 Γ— 10⁹³(94-digit number)
22379803838591676715…62690175493853093999
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
2.237 Γ— 10⁹³(94-digit number)
22379803838591676715…62690175493853093999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.237 Γ— 10⁹³(94-digit number)
22379803838591676715…62690175493853094001
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
4.475 Γ— 10⁹³(94-digit number)
44759607677183353431…25380350987706187999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.475 Γ— 10⁹³(94-digit number)
44759607677183353431…25380350987706188001
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
8.951 Γ— 10⁹³(94-digit number)
89519215354366706862…50760701975412375999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.951 Γ— 10⁹³(94-digit number)
89519215354366706862…50760701975412376001
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
1.790 Γ— 10⁹⁴(95-digit number)
17903843070873341372…01521403950824751999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.790 Γ— 10⁹⁴(95-digit number)
17903843070873341372…01521403950824752001
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
3.580 Γ— 10⁹⁴(95-digit number)
35807686141746682745…03042807901649503999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.580 Γ— 10⁹⁴(95-digit number)
35807686141746682745…03042807901649504001
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:57,949,177 XPMΒ·at block #6,838,102 Β· updates every 60s
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