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Block #2,224,977

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 7/27/2017, 8:11:07 AM Β· Difficulty 10.9474 Β· 4,600,420 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b4ea60fedf69217313955f6c62e72a87c6bb770da0e880a3e07eccaf9d26b22d
View on Chainz β†—

Height

#2,224,977

Difficulty

10.947376

Transactions

2

Size

394 B

Version

2

Bits

0af28737

Nonce

424,739,049

Timestamp

7/27/2017, 8:11:07 AM

Confirmations

4,600,420

Mined by

⛏️ P2SHAGqP8B5WeK23SsBMFvqAbrg6KiKX3TF24W

Merkle Root

abec9a74dd5d522aacad68991b3a9f1b62e67d4c2cf3c5381f523a80c129e755
Transactions (2)
Coinbase02889f514f4c08…80ac28a7c18dec
1 in β†’ 1 out8.3400 XPM110 B
AGqP8B5W…KX3TF24W
c723981348dd3e…0dc4cccc1597ee
1 in β†’ 1 out449.9900 XPM193 B
AHA9fN8X…KFsLBUfg
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.

3.720 Γ— 10⁹⁷(98-digit number)
37208781947729273382…07446353822150901759
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
3.720 Γ— 10⁹⁷(98-digit number)
37208781947729273382…07446353822150901759
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.720 Γ— 10⁹⁷(98-digit number)
37208781947729273382…07446353822150901761
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
7.441 Γ— 10⁹⁷(98-digit number)
74417563895458546765…14892707644301803519
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.441 Γ— 10⁹⁷(98-digit number)
74417563895458546765…14892707644301803521
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
1.488 Γ— 10⁹⁸(99-digit number)
14883512779091709353…29785415288603607039
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.488 Γ— 10⁹⁸(99-digit number)
14883512779091709353…29785415288603607041
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
2.976 Γ— 10⁹⁸(99-digit number)
29767025558183418706…59570830577207214079
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.976 Γ— 10⁹⁸(99-digit number)
29767025558183418706…59570830577207214081
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
5.953 Γ— 10⁹⁸(99-digit number)
59534051116366837412…19141661154414428159
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.953 Γ— 10⁹⁸(99-digit number)
59534051116366837412…19141661154414428161
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
1.190 Γ— 10⁹⁹(100-digit number)
11906810223273367482…38283322308828856319
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,847,276 XPMΒ·at block #6,825,396 Β· updates every 60s
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