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Block #2,623,283

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 4/21/2018, 6:37:12 AM Β· Difficulty 11.2185 Β· 4,214,499 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
9c89cffffb1a7d5f2c92fd3da2c342f9bcad2ac245ec243c858664821fd22aa9
View on Chainz β†—

Height

#2,623,283

Difficulty

11.218462

Transactions

1

Size

199 B

Version

2

Bits

0b37ed27

Nonce

373,805,631

Timestamp

4/21/2018, 6:37:12 AM

Confirmations

4,214,499

Mined by

⛏️ P2SHAGkzmSYoTEkjRjAiPvLvu81Srhs1MZNoyW

Merkle Root

1ef11c61d6ceb60bd5c501989cfedc728f7bb1270d99c862b3d3b1b43299a0ab
Transactions (1)
Coinbase1ef11c61d6ceb6…d3b1b43299a0ab
1 in β†’ 1 out7.9300 XPM109 B
AGkzmSYo…s1MZNoyW
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.

3.353 Γ— 10⁹⁴(95-digit number)
33539617173177659442…57340374548673436799
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
3.353 Γ— 10⁹⁴(95-digit number)
33539617173177659442…57340374548673436799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.353 Γ— 10⁹⁴(95-digit number)
33539617173177659442…57340374548673436801
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
6.707 Γ— 10⁹⁴(95-digit number)
67079234346355318885…14680749097346873599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
6.707 Γ— 10⁹⁴(95-digit number)
67079234346355318885…14680749097346873601
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
1.341 Γ— 10⁹⁡(96-digit number)
13415846869271063777…29361498194693747199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.341 Γ— 10⁹⁡(96-digit number)
13415846869271063777…29361498194693747201
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
2.683 Γ— 10⁹⁡(96-digit number)
26831693738542127554…58722996389387494399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.683 Γ— 10⁹⁡(96-digit number)
26831693738542127554…58722996389387494401
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
5.366 Γ— 10⁹⁡(96-digit number)
53663387477084255108…17445992778774988799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
5.366 Γ— 10⁹⁡(96-digit number)
53663387477084255108…17445992778774988801
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
1.073 Γ— 10⁹⁢(97-digit number)
10732677495416851021…34891985557549977599
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:57,946,593 XPMΒ·at block #6,837,781 Β· updates every 60s
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