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Block #941,430

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 2/18/2015, 5:43:24 AM Β· Difficulty 10.9018 Β· 5,865,542 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
32b5cbbf901f51bf38ea5c400712799569a24cf71550070734008a1da7f72eb3
View on Chainz β†—

Height

#941,430

Difficulty

10.901754

Transactions

2

Size

432 B

Version

2

Bits

0ae6d961

Nonce

161,819,639

Timestamp

2/18/2015, 5:43:24 AM

Confirmations

5,865,542

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

c62b3e3531ed7af0c4d017b80e3a69c2a58e301c959cd97e520428734c066ff3
Transactions (2)
Coinbase8810f174b99678…49b40c956fa0b3
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
c90927e75761df…8c53ec852a144f
1 in β†’ 2 out2.2127 XPM225 B
AP2fsmU4…Zg3DWqHCAf3aPj7K…cnGd5dnY
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.

2.447 Γ— 10⁹⁷(98-digit number)
24474396676048600414…36636556135943404799
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
2.447 Γ— 10⁹⁷(98-digit number)
24474396676048600414…36636556135943404799
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.447 Γ— 10⁹⁷(98-digit number)
24474396676048600414…36636556135943404801
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
4.894 Γ— 10⁹⁷(98-digit number)
48948793352097200829…73273112271886809599
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.894 Γ— 10⁹⁷(98-digit number)
48948793352097200829…73273112271886809601
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
9.789 Γ— 10⁹⁷(98-digit number)
97897586704194401658…46546224543773619199
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.789 Γ— 10⁹⁷(98-digit number)
97897586704194401658…46546224543773619201
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
1.957 Γ— 10⁹⁸(99-digit number)
19579517340838880331…93092449087547238399
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.957 Γ— 10⁹⁸(99-digit number)
19579517340838880331…93092449087547238401
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
3.915 Γ— 10⁹⁸(99-digit number)
39159034681677760663…86184898175094476799
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.915 Γ— 10⁹⁸(99-digit number)
39159034681677760663…86184898175094476801
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
7.831 Γ— 10⁹⁸(99-digit number)
78318069363355521327…72369796350188953599
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:57,699,876 XPMΒ·at block #6,806,971 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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