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Block #3,503,442

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/7/2020, 5:36:10 AM Β· Difficulty 10.9307 Β· 3,333,418 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e56e8ae651f110b920be5fcecffa14a9f536adaef8ff5d5522135426bb657a6a
View on Chainz β†—

Height

#3,503,442

Difficulty

10.930689

Transactions

1

Size

198 B

Version

2

Bits

0aee419d

Nonce

1,838,451,187

Timestamp

1/7/2020, 5:36:10 AM

Confirmations

3,333,418

Mined by

⛏️ P2SHAZAqcMBbXdmDRGExxahGhMujwqaZKXCHtA

Merkle Root

b55a574d45dfdb974ccfa307a35c21e3214e58448247a84b545a3367727fddc2
Transactions (1)
Coinbaseb55a574d45dfdb…5a3367727fddc2
1 in β†’ 1 out8.3600 XPM109 B
AZAqcMBb…aZKXCHtA
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.

1.877 Γ— 10⁹³(94-digit number)
18775236423748385320…48369583804983327499
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
1.877 Γ— 10⁹³(94-digit number)
18775236423748385320…48369583804983327499
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.877 Γ— 10⁹³(94-digit number)
18775236423748385320…48369583804983327501
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
3.755 Γ— 10⁹³(94-digit number)
37550472847496770641…96739167609966654999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.755 Γ— 10⁹³(94-digit number)
37550472847496770641…96739167609966655001
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
7.510 Γ— 10⁹³(94-digit number)
75100945694993541282…93478335219933309999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.510 Γ— 10⁹³(94-digit number)
75100945694993541282…93478335219933310001
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
1.502 Γ— 10⁹⁴(95-digit number)
15020189138998708256…86956670439866619999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.502 Γ— 10⁹⁴(95-digit number)
15020189138998708256…86956670439866620001
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
3.004 Γ— 10⁹⁴(95-digit number)
30040378277997416513…73913340879733239999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.004 Γ— 10⁹⁴(95-digit number)
30040378277997416513…73913340879733240001
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 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
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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:57,939,169 XPMΒ·at block #6,836,859 Β· updates every 60s
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