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Block #3,055,960

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/16/2019, 10:06:19 PM Β· Difficulty 11.0091 Β· 3,781,104 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
00c5ced6e4a73398a8ca8b3303e3da51a926cb0c41ba7a198fd896f2514f3983
View on Chainz β†—

Height

#3,055,960

Difficulty

11.009082

Transactions

2

Size

575 B

Version

2

Bits

0b025337

Nonce

803,461,734

Timestamp

2/16/2019, 10:06:19 PM

Confirmations

3,781,104

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

1f6329027c95861bb3148f5f258b0f9c673ce6d844405f6beba62f36de5d9739
Transactions (2)
Coinbase23b2b6e90d170a…19af58f081fa12
1 in β†’ 1 out8.2500 XPM110 B
AbXwmGxD…4XXYP765
8458381b2e3762…0891b10ff6c749
2 in β†’ 2 out523.5989 XPM374 B
AeTHTL7A…vT1872bkAUoTQ2TP…rZWkWS9F
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.

1.981 Γ— 10⁹⁢(97-digit number)
19811509152650951761…85871774098284881919
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
1.981 Γ— 10⁹⁢(97-digit number)
19811509152650951761…85871774098284881919
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.981 Γ— 10⁹⁢(97-digit number)
19811509152650951761…85871774098284881921
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
3.962 Γ— 10⁹⁢(97-digit number)
39623018305301903522…71743548196569763839
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.962 Γ— 10⁹⁢(97-digit number)
39623018305301903522…71743548196569763841
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
7.924 Γ— 10⁹⁢(97-digit number)
79246036610603807044…43487096393139527679
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.924 Γ— 10⁹⁢(97-digit number)
79246036610603807044…43487096393139527681
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
1.584 Γ— 10⁹⁷(98-digit number)
15849207322120761408…86974192786279055359
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.584 Γ— 10⁹⁷(98-digit number)
15849207322120761408…86974192786279055361
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
3.169 Γ— 10⁹⁷(98-digit number)
31698414644241522817…73948385572558110719
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.169 Γ— 10⁹⁷(98-digit number)
31698414644241522817…73948385572558110721
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
6.339 Γ— 10⁹⁷(98-digit number)
63396829288483045635…47896771145116221439
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:57,940,815 XPMΒ·at block #6,837,063 Β· updates every 60s
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