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Block #486,530

TWNLength 10ā˜…ā˜…ā˜†ā˜†ā˜†

Bi-Twin Chain Ā· Discovered 4/11/2014, 3:44:22 PM Ā· Difficulty 10.6271 Ā· 6,323,583 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
62097d705974f87301b7d3c98133648958003ad7a294957ed9ee3db51268a895
View on Chainz ā†—

Height

#486,530

Difficulty

10.627139

Transactions

1

Size

799 B

Version

2

Bits

0aa08c28

Nonce

2,031

Timestamp

4/11/2014, 3:44:22 PM

Confirmations

6,323,583

Mined by

ā›ļø laSHAQvZBsUoAqCaKecR1VEueWTuBchppgRZTJ

Merkle Root

12933d7fcb319f75f114691ee0b30db40960338aa67c8e645add6f519da5927d
Transactions (1)
Coinbase12933d7fcb319fā€¦dd6f519da5927d
1 in ā†’ 19 out8.8400 XPM709 B
AQvZBsUoā€¦hppgRZTJANNg88pGā€¦ppn21sTeAdxPNkWDā€¦ZMa9u34qAQ8QAT3Jā€¦rCFKuVbRATKK7iFzā€¦wZm46KN1
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) ā€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

4.647 Ɨ 10ā¹ā“(95-digit number)
46477877979729654613ā€¦31008231816746577919
Discovered Prime Numbers
Lower: 2^k Ɨ origin āˆ’ 1 | Upper: 2^k Ɨ 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 ā€” Twin Prime Pair (origin Ā± 1)
origin āˆ’ 1
4.647 Ɨ 10ā¹ā“(95-digit number)
46477877979729654613ā€¦31008231816746577919
Verify on FactorDB ā†—Wolfram Alpha ā†—
origin + 1
4.647 Ɨ 10ā¹ā“(95-digit number)
46477877979729654613ā€¦31008231816746577921
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: origin + 1 āˆ’ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 1 ā€” Twin Prime Pair (2^1 Ɨ origin Ā± 1)
2^1 Ɨ origin āˆ’ 1
9.295 Ɨ 10ā¹ā“(95-digit number)
92955755959459309227ā€¦62016463633493155839
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^1 Ɨ origin + 1
9.295 Ɨ 10ā¹ā“(95-digit number)
92955755959459309227ā€¦62016463633493155841
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^1 Ɨ origin + 1 āˆ’ 2^1 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 2 ā€” Twin Prime Pair (2^2 Ɨ origin Ā± 1)
2^2 Ɨ origin āˆ’ 1
1.859 Ɨ 10ā¹āµ(96-digit number)
18591151191891861845ā€¦24032927266986311679
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^2 Ɨ origin + 1
1.859 Ɨ 10ā¹āµ(96-digit number)
18591151191891861845ā€¦24032927266986311681
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^2 Ɨ origin + 1 āˆ’ 2^2 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 3 ā€” Twin Prime Pair (2^3 Ɨ origin Ā± 1)
2^3 Ɨ origin āˆ’ 1
3.718 Ɨ 10ā¹āµ(96-digit number)
37182302383783723691ā€¦48065854533972623359
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^3 Ɨ origin + 1
3.718 Ɨ 10ā¹āµ(96-digit number)
37182302383783723691ā€¦48065854533972623361
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^3 Ɨ origin + 1 āˆ’ 2^3 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)
Level 4 ā€” Twin Prime Pair (2^4 Ɨ origin Ā± 1)
2^4 Ɨ origin āˆ’ 1
7.436 Ɨ 10ā¹āµ(96-digit number)
74364604767567447382ā€¦96131709067945246719
Verify on FactorDB ā†—Wolfram Alpha ā†—
2^4 Ɨ origin + 1
7.436 Ɨ 10ā¹āµ(96-digit number)
74364604767567447382ā€¦96131709067945246721
Verify on FactorDB ā†—Wolfram Alpha ā†—
Difference: 2^4 Ɨ origin + 1 āˆ’ 2^4 Ɨ origin āˆ’ 1 = 2 (twin primes āœ“)

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 ā€” the large number shown above ā€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

ā˜…ā˜…ā˜†ā˜†ā˜†
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 Ɨ 3 Ɨ 5 Ɨ 7 Ɨ ā€¦), the result is the first prime in the chain. The origin is deliberately divisible by this primorial ā€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Ɨ Primorial (2Ā·3Ā·5Ā·7Ā·11Ā·ā€¦)
Source: Primecoin prime.cpp ā€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors ā€” 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 āˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,724,975 XPMĀ·at block #6,810,112 Ā· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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