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Block #1,832,032

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/1/2016, 10:41:30 PM Β· Difficulty 10.7208 Β· 5,012,076 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
5abf0dd920b2123ebc4fe45dae4ed77e5bcf0da89e4eccf7600431c16cced5b7
View on Chainz β†—

Height

#1,832,032

Difficulty

10.720801

Transactions

2

Size

390 B

Version

2

Bits

0ab8866f

Nonce

912,861,570

Timestamp

11/1/2016, 10:41:30 PM

Confirmations

5,012,076

Mined by

⛏️ P2SHAH2rLqkLd2XwVbGFm1ubSwVozmD5WZqJgJ

Merkle Root

5db786e79cc0697ad39a02ee0a05b6818506b6b8ffc2c99a0f7d9a0654af86c6
Transactions (2)
Coinbase6c74ace51569cd…690ef20ee7d62c
1 in β†’ 1 out8.7000 XPM109 B
AH2rLqkL…D5WZqJgJ
0cdbec757948a5…9357c4f3f679d3
1 in β†’ 1 out0.1395 XPM192 B
AUKV3Goi…ajcvvDKN
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.

3.977 Γ— 10⁹²(93-digit number)
39778636775991967782…07848352394495015119
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
3.977 Γ— 10⁹²(93-digit number)
39778636775991967782…07848352394495015119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
3.977 Γ— 10⁹²(93-digit number)
39778636775991967782…07848352394495015121
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
7.955 Γ— 10⁹²(93-digit number)
79557273551983935565…15696704788990030239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
7.955 Γ— 10⁹²(93-digit number)
79557273551983935565…15696704788990030241
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
1.591 Γ— 10⁹³(94-digit number)
15911454710396787113…31393409577980060479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.591 Γ— 10⁹³(94-digit number)
15911454710396787113…31393409577980060481
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
3.182 Γ— 10⁹³(94-digit number)
31822909420793574226…62786819155960120959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.182 Γ— 10⁹³(94-digit number)
31822909420793574226…62786819155960120961
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
6.364 Γ— 10⁹³(94-digit number)
63645818841587148452…25573638311920241919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
6.364 Γ— 10⁹³(94-digit number)
63645818841587148452…25573638311920241921
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
1.272 Γ— 10⁹⁴(95-digit number)
12729163768317429690…51147276623840483839
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:57,997,237 XPMΒ·at block #6,844,107 Β· updates every 60s
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