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Block #2,147,142

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 6/5/2017, 3:47:52 PM Β· Difficulty 10.8926 Β· 4,698,152 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4c5e04eade4e177fdde6a06f2d84d46bad248ce1e86758ca8371670911ea3cbe
View on Chainz β†—

Height

#2,147,142

Difficulty

10.892596

Transactions

1

Size

199 B

Version

2

Bits

0ae48131

Nonce

890,124,263

Timestamp

6/5/2017, 3:47:52 PM

Confirmations

4,698,152

Mined by

⛏️ P2SHAHadU7LRpPGwit9q6GGAkKEzeMofuwPf1w

Merkle Root

fb602205c626ad774889446e72cb451859e44355d9cbee590b795ecaf6de93e8
Transactions (1)
Coinbasefb602205c626ad…795ecaf6de93e8
1 in β†’ 1 out8.4100 XPM109 B
AHadU7LR…ofuwPf1w
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.

5.575 Γ— 10⁹³(94-digit number)
55754239981239842377…11596098539932354559
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
5.575 Γ— 10⁹³(94-digit number)
55754239981239842377…11596098539932354559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
5.575 Γ— 10⁹³(94-digit number)
55754239981239842377…11596098539932354561
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
1.115 Γ— 10⁹⁴(95-digit number)
11150847996247968475…23192197079864709119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.115 Γ— 10⁹⁴(95-digit number)
11150847996247968475…23192197079864709121
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
2.230 Γ— 10⁹⁴(95-digit number)
22301695992495936950…46384394159729418239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.230 Γ— 10⁹⁴(95-digit number)
22301695992495936950…46384394159729418241
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
4.460 Γ— 10⁹⁴(95-digit number)
44603391984991873901…92768788319458836479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.460 Γ— 10⁹⁴(95-digit number)
44603391984991873901…92768788319458836481
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
8.920 Γ— 10⁹⁴(95-digit number)
89206783969983747803…85537576638917672959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
8.920 Γ— 10⁹⁴(95-digit number)
89206783969983747803…85537576638917672961
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
1.784 Γ— 10⁹⁡(96-digit number)
17841356793996749560…71075153277835345919
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:58,006,790 XPMΒ·at block #6,845,293 Β· updates every 60s
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